Strong Quantum Mpemba Effect from Exact Slow-Mode Selection in Constrained Rydberg Chains

How can certain initial states in open quantum many-body systems relax to equilibrium faster than states that are closer to the steady state? The authors investigate whether this 'strong quantum Mpemba effect' can be explained by a general principle of Liouvillian mode selection rather than relying on specific, fine-tuned wave functions.

The researchers analyze constrained Rydberg chains, such as the PXP model and its generalizations, under local dephasing. They utilize the Liouvillian superoperator framework to identify the decay modes of the system. By examining the symmetry properties of the Hamiltonian and the initial density matrix, they derive a selection rule: if an initial state is translationally invariant and has a vanishing energy expectation (Tr(Hρ) = 0), it becomes 'blind' to the slowest decay channel—the Hamiltonian itself—thereby forcing the system to relax through faster available modes.

The study reveals that the Hamiltonian is an exact left Liouvillian slow mode in these constrained systems. A thermal state typically has a non-zero energy expectation and thus couples to this slow mode, leading to slower relaxation. In contrast, selected states (such as specific scar eigenstates, product states, or cat states) that satisfy the symmetry and energy conditions effectively remove this slow channel. This mechanism is shown to be robust across various constrained models, including longer-range blockade families and the (2,3) model, suggesting that exact slow-mode selection is a fundamental organizing principle for anomalous relaxation in these systems.

This work provides a clear, physically intuitive mechanism for the quantum Mpemba effect that does not require fine-tuned initial conditions. It demonstrates that anomalous relaxation is a consequence of the interplay between the system's constraints, symmetry, and the structure of the Liouvillian. These findings are highly relevant for experimental Rydberg atom platforms, where dephasing is often present and can be leveraged to engineer faster relaxation or control nonequilibrium dynamics.